/**
 * https://leetcode.cn/problems/minimum-insertion-steps-to-make-a-string-palindrome/submissions/581460307/
 * 1312.让字符串成为回文串的最少插入次数 1787
 * difficulty 陈贝纯 11.18
 * 区间dp
 */

class Solution {
public:
    int minInsertions(string s) {
        int n=s.size();
        vector<vector<int>> dp(n,vector<int>(n));
        for(int i=n-1;i>=0;--i){
            dp[i][i]=1;
            for(int j=i+1;j<n;++j){
                if(s[i]==s[j])
                dp[i][j]=dp[i+1][j-1]+2;
                else
                dp[i][j]=max(dp[i+1][j],dp[i][j-1]);
            }
        }
        return n-dp[0][n-1];
    }
};